Question

I) Hence solve cosec 3y ÷ cot 3y + tan 3y = 0.5 for 0

Answer 1

The value of y is π/9 or 7π/9 for the range 0 ≤ y ≤ π.

cosec 3y /( cot 3y + tan 3y) = 0.5

Trigonometry formula is:

cosec Ф = 1/ sin Ф

cot Ф = cos Ф/ sinФ

tan Ф = sinФ/ cos Ф

$\frac{\frac{1}{sin 3y} }{\frac{cos 3y}{sin 3y} +\frac{sin 3y}{cos 3y} }$  = 0.5

$\frac{\frac{1}{sin 3y} }{\frac{cos 3y^{2} + sin 3y^{2} }{sin 3y cos 3y} }$ = 0.5

sin² 3y + cos ² 3y = 1

1/ sin 3y × sin 3y cos 3y = 0.5

cos 3y = 0.5 = 1/2

cos π/ 3 = 1/2

For 0≤ y ≤π

0 ≤3y ≤ 3π

So 3y = 2kπ + π/3 , k = 0, 1

y = π/ 9 or 7π/ 9

Therefore the value of y is π/9 and 7π/ 9 for the given range.

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